The value function of singularly perturbed control systems

Z. Artstein; V. Gaitsgory

doi:10.1007/s002459911022

The value function of singularly perturbed control systems

Z. Artstein^*, V. Gaitsgory

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

58 Citations (Scopus)

Abstract

The limit as ε → 0 of the value function of a singularly perturbed optimal control problem is characterized. Under general conditions it is shown that limit value functions exist and solve in a viscosity sense a Hamilton-Jacobi equation. The Hamiltonian of this equation is generated by an infinite horizon optimization on the fast time scale. In particular, the limit Hamiltonian and the limit Hamilton-Jacobi equation are applicable in cases where the reduction of order, namely setting ε = 0, does not yield an optimal behavior.

Original language	English
Pages (from-to)	425-445
Number of pages	21
Journal	Applied Mathematics and Optimization
Volume	41
Issue number	3
DOIs	https://doi.org/10.1007/s002459911022
Publication status	Published - May 2000
Externally published	Yes

Keywords

Hamilton-jacobi equation
Limit hamiltonian
Optimal control
Singular perturbation

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10.1007/s002459911022

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KW - Singular perturbation

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The value function of singularly perturbed control systems

Abstract

Keywords

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